Question: Solve for $x$ and $y$ using substitution. ${6x+5y = 3}$ ${x = -y-1}$
Solution: Since $x$ has already been solved for, substitute $-y-1$ for $x$ in the first equation. ${6}{(-y-1)}{+ 5y = 3}$ Simplify and solve for $y$ $-6y-6 + 5y = 3$ $-y-6 = 3$ $-y-6{+6} = 3{+6}$ $-y = 9$ $\dfrac{-y}{{-1}} = \dfrac{9}{{-1}}$ ${y = -9}$ Now that you know ${y = -9}$ , plug it back into $\thinspace {x = -y-1}\thinspace$ to find $x$ ${x = -}{(-9)}{ - 1}$ $x = 9 - 1$ ${x = 8}$ You can also plug ${y = -9}$ into $\thinspace {6x+5y = 3}\thinspace$ and get the same answer for $x$ : ${6x + 5}{(-9)}{= 3}$ ${x = 8}$